The impact of stochastic lead times on the bullwhip effect–a theoretical insight

In this article, we analyze the models quantifying the bullwhip effect in supply chains with stochastic lead times and find advantages and disadvantages of their approaches to the bullwhip problem. Moreover, using computer simulation, we find interesting insights into the bullwhip behavior for a particular instance of a multi-echelon supply chain with constant customer demands and random lead times. We confirm the recent finding of Michna and Nielsen that under certain circumstances lead time signal processing is by itself a fundamental cause of bullwhip effect just like demand-signal processing is. The simulation also shows that in this supply chain the delay parameter of demand forecasting smooths the bullwhip effect at the manufacturer level much faster than the delay parameter of lead time forecasting. Additionally, in the supply chain with random demands, the reverse behavior is observed, that is, the delay parameter of lead time forecasting smooths bullwhip effect at the retailer stage much faster than the delay parameter of demand forecasting. At the manufacturer level, the delay parameter of demand forecasting and the delay parameter of lead time forecasting dampen the effect with a similar strength.